LMFDB - Embedded newform 5.34.b.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,34,Mod(4,5)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 34, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.4914144405$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26286285043 x^{14} + \cdots + 16\!\cdots\!36 $ x^16 + 26286285043x^14 + 277176279803774573548x^12 + 1496006322727341104924267746816x^10 + 4376228902975645752284567792282218577920x^8 + 6785210496827316795155770011788917433647451078656x^6 + 5093319366938751307797338793282286802764384084972313509888x^4 + 1608229292592013531797229664939538769264311330074914543142623510528*x^2 + 163532475457876517394407745867705361011086521692855999713211555842344615936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.11
Root			$31348.8i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+62697.7i q^{2} -3.24591e7i q^{3} +4.65894e9 q^{4} +(1.34579e11 + 3.13534e11i) q^{5} +2.03511e12 q^{6} +2.03055e13i q^{7} +8.30673e14i q^{8} +4.50547e15 q^{9} +O(q^{10})$	\(q+62697.7i q^{2} -3.24591e7i q^{3} +4.65894e9 q^{4} +(1.34579e11 + 3.13534e11i) q^{5} +2.03511e12 q^{6} +2.03055e13i q^{7} +8.30673e14i q^{8} +4.50547e15 q^{9} +(-1.96579e16 + 8.43781e15i) q^{10} -1.08204e17 q^{11} -1.51225e17i q^{12} -2.32496e17i q^{13} -1.27311e18 q^{14} +(1.01770e19 - 4.36832e18i) q^{15} -1.20613e19 q^{16} +2.21357e19i q^{17} +2.82482e20i q^{18} +2.01169e21 q^{19} +(6.26996e20 + 1.46074e21i) q^{20} +6.59098e20 q^{21} -6.78414e21i q^{22} +7.09891e21i q^{23} +2.69629e22 q^{24} +(-8.01921e22 + 8.43905e22i) q^{25} +1.45770e22 q^{26} -3.26686e23i q^{27} +9.46020e22i q^{28} -1.18108e24 q^{29} +(2.73884e23 + 6.38077e23i) q^{30} -9.41403e23 q^{31} +6.37921e24i q^{32} +3.51220e24i q^{33} -1.38786e24 q^{34} +(-6.36647e24 + 2.73270e24i) q^{35} +2.09907e25 q^{36} +1.19059e26i q^{37} +1.26128e26i q^{38} -7.54661e24 q^{39} +(-2.60445e26 + 1.11791e26i) q^{40} -5.26633e26 q^{41} +4.13239e25i q^{42} +1.00685e27i q^{43} -5.04115e26 q^{44} +(6.06343e26 + 1.41262e27i) q^{45} -4.45085e26 q^{46} +3.06131e27i q^{47} +3.91500e26i q^{48} +7.31868e27 q^{49} +(-5.29109e27 - 5.02786e27i) q^{50} +7.18505e26 q^{51} -1.08318e27i q^{52} -2.92557e28i q^{53} +2.04824e28 q^{54} +(-1.45620e28 - 3.39257e28i) q^{55} -1.68672e28 q^{56} -6.52976e28i q^{57} -7.40509e28i q^{58} +9.11668e28 q^{59} +(4.74142e28 - 2.03517e28i) q^{60} +2.27634e29 q^{61} -5.90238e28i q^{62} +9.14857e28i q^{63} -5.03568e29 q^{64} +(7.28955e28 - 3.12892e28i) q^{65} -2.20207e29 q^{66} +2.33634e30i q^{67} +1.03129e29i q^{68} +2.30424e29 q^{69} +(-1.71334e29 - 3.99163e29i) q^{70} -3.44979e30 q^{71} +3.74257e30i q^{72} -3.16717e29i q^{73} -7.46471e30 q^{74} +(2.73924e30 + 2.60296e30i) q^{75} +9.37233e30 q^{76} -2.19713e30i q^{77} -4.73155e29i q^{78} +1.55504e31 q^{79} +(-1.62321e30 - 3.78165e30i) q^{80} +1.44422e31 q^{81} -3.30187e31i q^{82} -5.93046e31i q^{83} +3.07069e30 q^{84} +(-6.94030e30 + 2.97901e30i) q^{85} -6.31272e31 q^{86} +3.83367e31i q^{87} -8.98822e31i q^{88} +1.27051e32 q^{89} +(-8.85679e31 + 3.80163e31i) q^{90} +4.72095e30 q^{91} +3.30734e31i q^{92} +3.05571e31i q^{93} -1.91937e32 q^{94} +(2.70732e32 + 6.30733e32i) q^{95} +2.07063e32 q^{96} +1.84352e32i q^{97} +4.58864e32i q^{98} -4.87509e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			62697.7i			0.676482i	0.941059	+	0.338241i	$0.109832\pi$
$2$			62697.7i			0.676482i	−0.941059	+	0.338241i	$0.890168\pi$
$3$		−	3.24591e7i		−	0.435347i	−0.976022	−	0.217674i	$-0.930153\pi$
$3$		−	3.24591e7i		−	0.435347i	0.976022	−	0.217674i	$-0.0698468\pi$
$4$	4.65894e9			0.542371
$5$	1.34579e11	+	3.13534e11i	0.394433	+	0.918925i
$5$	1.34579e11	+	3.13534e11i	0.394433	+	0.918925i
$6$	2.03511e12			0.294505
$7$			2.03055e13i			0.230938i	0.993311	+	0.115469i	$0.0368371\pi$
$7$			2.03055e13i			0.230938i	−0.993311	+	0.115469i	$0.963163\pi$
$8$			8.30673e14i			1.04339i
$9$	4.50547e15			0.810473
$10$	−1.96579e16	+	8.43781e15i	−0.621636	+	0.266827i
$11$	−1.08204e17			−0.710009			−0.355005	−	0.934865i	$-0.615521\pi$
$11$	−1.08204e17			−0.710009			−0.355005	+	0.934865i	$0.615521\pi$
$12$		−	1.51225e17i		−	0.236120i
$13$		−	2.32496e17i		−	0.0969059i	−0.998825	−	0.0484529i	$-0.984571\pi$
$13$		−	2.32496e17i		−	0.0969059i	0.998825	−	0.0484529i	$-0.0154291\pi$
$14$	−1.27311e18			−0.156226
$15$	1.01770e19	−	4.36832e18i	0.400051	−	0.171715i
$16$	−1.20613e19			−0.163462
$17$			2.21357e19i			0.110328i	0.998477	+	0.0551641i	$0.0175682\pi$
$17$			2.21357e19i			0.110328i	−0.998477	+	0.0551641i	$0.982432\pi$
$18$			2.82482e20i			0.548271i
$19$	2.01169e21			1.60002			0.800012	−	0.599984i	$-0.204827\pi$
$19$	2.01169e21			1.60002			0.800012	+	0.599984i	$0.204827\pi$
$20$	6.26996e20	+	1.46074e21i	0.213929	+	0.498399i
$21$	6.59098e20			0.100538
$22$		−	6.78414e21i		−	0.480309i
$23$			7.09891e21i			0.241370i	0.992691	+	0.120685i	$0.0385090\pi$
$23$			7.09891e21i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$24$	2.69629e22			0.454236
$25$	−8.01921e22	+	8.43905e22i	−0.688845	+	0.724908i
$26$	1.45770e22			0.0655551
$27$		−	3.26686e23i		−	0.788184i
$28$			9.46020e22i			0.125254i
$29$	−1.18108e24			−0.876419			−0.438209	−	0.898873i	$-0.644387\pi$
$29$	−1.18108e24			−0.876419			−0.438209	+	0.898873i	$0.644387\pi$
$30$	2.73884e23	+	6.38077e23i	0.116162	+	0.270628i
$31$	−9.41403e23			−0.232438			−0.116219	−	0.993224i	$-0.537078\pi$
$31$	−9.41403e23			−0.232438			−0.116219	+	0.993224i	$0.537078\pi$
$32$			6.37921e24i			0.932808i
$33$			3.51220e24i			0.309100i
$34$	−1.38786e24			−0.0746350
$35$	−6.36647e24	+	2.73270e24i	−0.212215	+	0.0910897i
$36$	2.09907e25			0.439577
$37$			1.19059e26i			1.58647i	0.608913	+	0.793237i	$0.291606\pi$
$37$			1.19059e26i			1.58647i	−0.608913	+	0.793237i	$0.708394\pi$
$38$			1.26128e26i			1.08239i
$39$	−7.54661e24			−0.0421877
$40$	−2.60445e26	+	1.11791e26i	−0.958794	+	0.411546i
$41$	−5.26633e26			−1.28996			−0.644978	−	0.764201i	$-0.723133\pi$
$41$	−5.26633e26			−1.28996			−0.644978	+	0.764201i	$0.723133\pi$
$42$			4.13239e25i			0.0680124i
$43$			1.00685e27i			1.12392i	0.827165	+	0.561960i	$0.189952\pi$
$43$			1.00685e27i			1.12392i	−0.827165	+	0.561960i	$0.810048\pi$
$44$	−5.04115e26			−0.385089
$45$	6.06343e26	+	1.41262e27i	0.319677	+	0.744763i
$46$	−4.45085e26			−0.163282
$47$			3.06131e27i			0.787577i	0.919201	+	0.393788i	$0.128836\pi$
$47$			3.06131e27i			0.787577i	−0.919201	+	0.393788i	$0.871164\pi$
$48$			3.91500e26i			0.0711626i
$49$	7.31868e27			0.946668
$50$	−5.29109e27	−	5.02786e27i	−0.490388	−	0.465992i
$51$	7.18505e26			0.0480310
$52$		−	1.08318e27i		−	0.0525590i
$53$		−	2.92557e28i		−	1.03671i	−0.855165	−	0.518356i	$-0.826544\pi$
$53$		−	2.92557e28i		−	1.03671i	0.855165	−	0.518356i	$-0.173456\pi$
$54$	2.04824e28			0.533193
$55$	−1.45620e28	−	3.39257e28i	−0.280051	−	0.652445i
$56$	−1.68672e28			−0.240958
$57$		−	6.52976e28i		−	0.696566i
$58$		−	7.40509e28i		−	0.592882i
$59$	9.11668e28			0.550527			0.275263	−	0.961369i	$-0.411235\pi$
$59$	9.11668e28			0.550527			0.275263	+	0.961369i	$0.411235\pi$
$60$	4.74142e28	−	2.03517e28i	0.216976	−	0.0931335i
$61$	2.27634e29			0.793038			0.396519	−	0.918026i	$-0.370218\pi$
$61$	2.27634e29			0.793038			0.396519	+	0.918026i	$0.370218\pi$
$62$		−	5.90238e28i		−	0.157240i
$63$			9.14857e28i			0.187169i
$64$	−5.03568e29			−0.794490
$65$	7.28955e28	−	3.12892e28i	0.0890492	−	0.0382229i
$66$	−2.20207e29			−0.209101
$67$			2.33634e30i			1.73102i	0.500889	+	0.865511i	$0.333006\pi$
$67$			2.33634e30i			1.73102i	−0.500889	+	0.865511i	$0.666994\pi$
$68$			1.03129e29i			0.0598388i
$69$	2.30424e29			0.105080
$70$	−1.71334e29	−	3.99163e29i	−0.0616206	−	0.143560i
$71$	−3.44979e30			−0.981814			−0.490907	−	0.871212i	$-0.663335\pi$
$71$	−3.44979e30			−0.981814			−0.490907	+	0.871212i	$0.663335\pi$
$72$			3.74257e30i			0.845637i
$73$		−	3.16717e29i		−	0.0569960i	−0.999594	−	0.0284980i	$-0.990928\pi$
$73$		−	3.16717e29i		−	0.0569960i	0.999594	−	0.0284980i	$-0.00907243\pi$
$74$	−7.46471e30			−1.07322
$75$	2.73924e30	+	2.60296e30i	0.315587	+	0.299887i
$76$	9.37233e30			0.867807
$77$		−	2.19713e30i		−	0.163968i
$78$		−	4.73155e29i		−	0.0285392i
$79$	1.55504e31			0.760141			0.380070	−	0.924958i	$-0.375900\pi$
$79$	1.55504e31			0.760141			0.380070	+	0.924958i	$0.375900\pi$
$80$	−1.62321e30	−	3.78165e30i	−0.0644747	−	0.150209i
$81$	1.44422e31			0.467339
$82$		−	3.30187e31i		−	0.872632i
$83$		−	5.93046e31i		−	1.28322i	−0.767033	−	0.641608i	$-0.778268\pi$
$83$		−	5.93046e31i		−	1.28322i	0.767033	−	0.641608i	$-0.221732\pi$
$84$	3.07069e30			0.0545291
$85$	−6.94030e30	+	2.97901e30i	−0.101383	+	0.0435171i
$86$	−6.31272e31			−0.760312
$87$			3.83367e31i			0.381547i
$88$		−	8.98822e31i		−	0.740814i
$89$	1.27051e32			0.869050			0.434525	−	0.900660i	$-0.356916\pi$
$89$	1.27051e32			0.869050			0.434525	+	0.900660i	$0.356916\pi$
$90$	−8.85679e31	+	3.80163e31i	−0.503819	+	0.216256i
$91$	4.72095e30			0.0223793
$92$			3.30734e31i			0.130912i
$93$			3.05571e31i			0.101191i
$94$	−1.91937e32			−0.532782
$95$	2.70732e32	+	6.30733e32i	0.631102	+	1.47030i
$96$	2.07063e32			0.406095
$97$			1.84352e32i			0.304729i	0.988324	+	0.152365i	$0.0486888\pi$
$97$			1.84352e32i			0.304729i	−0.988324	+	0.152365i	$0.951311\pi$
$98$			4.58864e32i			0.640404i
$99$	−4.87509e32			−0.575443
$100$	−3.73610e32	+	3.93170e32i	−0.373610	+	0.393170i
$101$	−1.05952e33			−0.899101			−0.449550	−	0.893255i	$-0.648416\pi$
$101$	−1.05952e33			−0.899101			−0.449550	+	0.893255i	$0.648416\pi$
$102$			4.50486e31i			0.0324922i
$103$		−	2.58769e33i		−	1.58891i	−0.607325	−	0.794454i	$-0.707757\pi$
$103$		−	2.58769e33i		−	1.58891i	0.607325	−	0.794454i	$-0.292243\pi$
$104$	1.93128e32			0.101110
$105$	8.87009e31	+	2.06650e32i	0.0396556	+	0.0923871i
$106$	1.83426e33			0.701317
$107$			1.25320e33i			0.410383i	0.978722	+	0.205191i	$0.0657817\pi$
$107$			1.25320e33i			0.410383i	−0.978722	+	0.205191i	$0.934218\pi$
$108$		−	1.52201e33i		−	0.427489i
$109$	−4.85391e32			−0.117099			−0.0585497	−	0.998284i	$-0.518648\pi$
$109$	−4.85391e32			−0.117099			−0.0585497	+	0.998284i	$0.518648\pi$
$110$	2.12706e33	−	9.13005e32i	0.441368	−	0.189450i
$111$	3.86454e33			0.690667
$112$		−	2.44912e32i		−	0.0377496i
$113$		−	1.19302e34i		−	1.58801i	−0.607908	−	0.794007i	$-0.707991\pi$
$113$		−	1.19302e34i		−	1.58801i	0.607908	−	0.794007i	$-0.292009\pi$
$114$	4.09401e33			0.471215
$115$	−2.22575e33	+	9.55367e32i	−0.221800	+	0.0952041i
$116$	−5.50257e33			−0.475345
$117$		−	1.04750e33i		−	0.0785396i
$118$			5.71594e33i			0.372422i
$119$	−4.49476e32			−0.0254790
$120$	3.62865e33	+	8.45380e33i	0.179166	+	0.417408i
$121$	−1.15171e34			−0.495887
$122$			1.42721e34i			0.536476i
$123$			1.70940e34i			0.561578i
$124$	−4.38594e33			−0.126068
$125$	−3.72515e34	−	1.37858e34i	−0.937840	−	0.347069i
$126$	−5.73594e33			−0.126617
$127$			3.24467e34i			0.628650i	0.949315	+	0.314325i	$0.101778\pi$
$127$			3.24467e34i			0.628650i	−0.949315	+	0.314325i	$0.898222\pi$
$128$			2.32245e34i			0.395350i
$129$	3.26814e34			0.489295
$130$	1.96176e33	+	4.57038e33i	0.0258571	+	0.0602402i
$131$	7.67974e34			0.892010			0.446005	−	0.895030i	$-0.352846\pi$
$131$	7.67974e34			0.892010			0.446005	+	0.895030i	$0.352846\pi$
$132$			1.63631e34i			0.167647i
$133$			4.08483e34i			0.369507i
$134$	−1.46483e35			−1.17101
$135$	1.02427e35	−	4.39651e34i	0.724282	−	0.310886i
$136$	−1.83875e34			−0.115115
$137$		−	3.25139e35i		−	1.80377i	−0.431980	−	0.901883i	$-0.642185\pi$
$137$		−	3.25139e35i		−	1.80377i	0.431980	−	0.901883i	$-0.357815\pi$
$138$			1.44471e34i			0.0710845i
$139$	1.06447e35			0.464933			0.232466	−	0.972604i	$-0.425320\pi$
$139$	1.06447e35			0.464933			0.232466	+	0.972604i	$0.425320\pi$
$140$	−2.96610e34	+	1.27315e34i	−0.115099	+	0.0494044i
$141$	9.93674e34			0.342869
$142$		−	2.16294e35i		−	0.664180i
$143$			2.51570e34i			0.0688041i
$144$	−5.43420e34			−0.132481
$145$	−1.58949e35	−	3.70309e35i	−0.345689	−	0.805363i
$146$	1.98574e34			0.0385568
$147$		−	2.37558e35i		−	0.412129i
$148$			5.54687e35i			0.860458i
$149$	3.66491e33			0.00508733			0.00254366	−	0.999997i	$-0.499190\pi$
$149$	3.66491e33			0.00508733			0.00254366	+	0.999997i	$0.499190\pi$
$150$	−1.63200e35	+	1.71744e35i	−0.202868	+	0.213489i
$151$	5.64872e35			0.629261			0.314630	−	0.949214i	$-0.398119\pi$
$151$	5.64872e35			0.629261			0.314630	+	0.949214i	$0.398119\pi$
$152$			1.67106e36i			1.66944i
$153$			9.97317e34i			0.0894179i
$154$	1.37755e35			0.110922
$155$	−1.26693e35	−	2.95162e35i	−0.0916814	−	0.213593i
$156$	−3.51592e34			−0.0228814
$157$		−	1.11445e34i		−	0.00652702i	−0.999995	−	0.00326351i	$-0.998961\pi$
$157$		−	1.11445e34i		−	0.00652702i	0.999995	−	0.00326351i	$-0.00103881\pi$
$158$			9.74973e35i			0.514222i
$159$	−9.49612e35			−0.451329
$160$	−2.00010e36	+	8.58510e35i	−0.857181	+	0.367930i
$161$	−1.44147e35			−0.0557415
$162$			9.05496e35i			0.316147i
$163$		−	2.92217e36i		−	0.921742i	−0.887467	−	0.460871i	$-0.847537\pi$
$163$		−	2.92217e36i		−	0.921742i	0.887467	−	0.460871i	$-0.152463\pi$
$164$	−2.45355e36			−0.699635
$165$	−1.10120e36	+	4.72670e35i	−0.284040	+	0.121919i
$166$	3.71826e36			0.868073
$167$		−	3.59336e36i		−	0.759764i	−0.925035	−	0.379882i	$-0.875965\pi$
$167$		−	3.59336e36i		−	0.759764i	0.925035	−	0.379882i	$-0.124035\pi$
$168$			5.47495e35i			0.104900i
$169$	5.70208e36			0.990609
$170$	−1.86777e35	−	4.35141e35i	−0.0294385	−	0.0685840i
$171$	9.06360e36			1.29678
$172$			4.69085e36i			0.609582i
$173$		−	1.66997e37i		−	1.97218i	−0.166201	−	0.986092i	$-0.553150\pi$
$173$		−	1.66997e37i		−	1.97218i	0.166201	−	0.986092i	$-0.446850\pi$
$174$	−2.40362e36			−0.258110
$175$	−1.71359e36	−	1.62834e36i	−0.167409	−	0.159081i
$176$	1.30509e36			0.116059
$177$		−	2.95919e36i		−	0.239670i
$178$			7.96583e36i			0.587897i
$179$	−2.30603e37			−1.55164			−0.775818	−	0.630957i	$-0.782663\pi$
$179$	−2.30603e37			−1.55164			−0.775818	+	0.630957i	$0.782663\pi$
$180$	2.82491e36	+	6.58130e36i	0.173384	+	0.403938i
$181$	2.49511e37			1.39763			0.698815	−	0.715302i	$-0.253711\pi$
$181$	2.49511e37			1.39763			0.698815	+	0.715302i	$0.253711\pi$
$182$			2.95992e35i			0.0151392i
$183$		−	7.38878e36i		−	0.345247i
$184$	−5.89688e36			−0.251842
$185$	−3.73290e37	+	1.60228e37i	−1.45785	+	0.625758i
$186$	−1.91586e36			−0.0684542
$187$		−	2.39517e36i		−	0.0783340i
$188$			1.42625e37i			0.427159i
$189$	6.63351e36			0.182022
$190$	−3.95455e37	+	1.69742e37i	−0.994633	+	0.426929i
$191$	6.59976e37			1.52222			0.761110	−	0.648622i	$-0.224655\pi$
$191$	6.59976e37			1.52222			0.761110	+	0.648622i	$0.224655\pi$
$192$			1.63454e37i			0.345879i
$193$			5.32383e37i			1.03402i	0.855980	+	0.517010i	$0.172955\pi$
$193$			5.32383e37i			1.03402i	−0.855980	+	0.517010i	$0.827045\pi$
$194$	−1.15584e37			−0.206144
$195$	−1.01562e36	−	2.36612e36i	−0.0166402	−	0.0387673i
$196$	3.40973e37			0.513445
$197$			6.19936e36i			0.0858330i	0.999079	+	0.0429165i	$0.0136649\pi$
$197$			6.19936e36i			0.0858330i	−0.999079	+	0.0429165i	$0.986335\pi$
$198$		−	3.05657e37i		−	0.389277i
$199$	−2.13198e37			−0.249866			−0.124933	−	0.992165i	$-0.539872\pi$
$199$	−2.13198e37			−0.249866			−0.124933	+	0.992165i	$0.539872\pi$
$200$	−7.01009e37	−	6.66135e37i	−0.756360	−	0.718732i
$201$	7.58357e37			0.753596
$202$		−	6.64297e37i		−	0.608226i
$203$		−	2.39824e37i		−	0.202399i
$204$	3.34747e36			0.0260507
$205$	−7.08739e37	−	1.65118e38i	−0.508801	−	1.18537i
$206$	1.62242e38			1.07487
$207$			3.19839e37i			0.195624i
$208$			2.80421e36i			0.0158404i
$209$	−2.17673e38			−1.13603
$210$	−1.29565e37	+	5.56134e36i	−0.0624983	+	0.0268263i
$211$	3.45541e38			1.54113			0.770566	−	0.637361i	$-0.219974\pi$
$211$	3.45541e38			1.54113			0.770566	+	0.637361i	$0.219974\pi$
$212$		−	1.36300e38i		−	0.562283i
$213$			1.11977e38i			0.427430i
$214$	−7.85729e37			−0.277617
$215$	−3.15682e38	+	1.35501e38i	−1.03280	+	0.443311i
$216$	2.71369e38			0.822381
$217$		−	1.91157e37i		−	0.0536789i
$218$		−	3.04329e37i		−	0.0792157i
$219$	−1.02804e37			−0.0248131
$220$	−6.78435e37	−	1.58057e38i	−0.151892	−	0.353867i
$221$	5.14646e36			0.0106914
$222$			2.42298e38i			0.467224i
$223$			7.52757e38i			1.34780i	0.738824	+	0.673899i	$0.235382\pi$
$223$			7.52757e38i			1.34780i	−0.738824	+	0.673899i	$0.764618\pi$
$224$	−1.29533e38			−0.215421
$225$	−3.61303e38	+	3.80218e38i	−0.558290	+	0.587519i
$226$	7.47998e38			1.07426
$227$			8.77387e38i			1.17156i	0.810470	+	0.585780i	$0.199212\pi$
$227$			8.77387e38i			1.17156i	−0.810470	+	0.585780i	$0.800788\pi$
$228$		−	3.04217e38i		−	0.377797i
$229$	−1.04883e39			−1.21177			−0.605887	−	0.795551i	$-0.707182\pi$
$229$	−1.04883e39			−1.21177			−0.605887	+	0.795551i	$0.707182\pi$
$230$	−5.98993e37	−	1.39550e38i	−0.0644039	−	0.150044i
$231$	−7.13170e37			−0.0713831
$232$		−	9.81090e38i		−	0.914444i
$233$		−	9.75026e38i		−	0.846532i	−0.906005	−	0.423266i	$-0.860884\pi$
$233$		−	9.75026e38i		−	0.846532i	0.906005	−	0.423266i	$-0.139116\pi$
$234$	6.56760e37			0.0531307
$235$	−9.59826e38	+	4.11989e38i	−0.723724	+	0.310646i
$236$	4.24740e38			0.298590
$237$		−	5.04751e38i		−	0.330925i
$238$		−	2.81811e37i		−	0.0172361i
$239$	2.23598e39			1.27615			0.638076	−	0.769973i	$-0.279731\pi$
$239$	2.23598e39			1.27615			0.638076	+	0.769973i	$0.279731\pi$
$240$	−1.22749e38	+	5.26879e37i	−0.0653931	+	0.0280689i
$241$	8.11623e38			0.403713			0.201857	−	0.979415i	$-0.435302\pi$
$241$	8.11623e38			0.403713			0.201857	+	0.979415i	$0.435302\pi$
$242$		−	7.22093e38i		−	0.335459i
$243$		−	2.28485e39i		−	0.991639i
$244$	1.06053e39			0.430121
$245$	9.84943e38	+	2.29466e39i	0.373397	+	0.869916i
$246$	−1.07176e39			−0.379898
$247$		−	4.67710e38i		−	0.155052i
$248$		−	7.81999e38i		−	0.242523i
$249$	−1.92497e39			−0.558644
$250$	8.64336e38	−	2.33558e39i	0.234786	−	0.634432i
$251$	3.08797e39			0.785338			0.392669	−	0.919680i	$-0.371552\pi$
$251$	3.08797e39			0.785338			0.392669	+	0.919680i	$0.371552\pi$
$252$			4.26226e38i			0.101515i
$253$		−	7.68131e38i		−	0.171375i
$254$	−2.03433e39			−0.425271
$255$	9.66959e37	+	2.25276e38i	0.0189450	+	0.0441369i
$256$	−5.78174e39			−1.06194
$257$			7.37117e39i			1.26952i	0.772709	+	0.634761i	$0.218901\pi$
$257$			7.37117e39i			1.26952i	−0.772709	+	0.634761i	$0.781099\pi$
$258$			2.04905e39i			0.331000i
$259$	−2.41755e39			−0.366377
$260$	3.39615e38	−	1.45774e38i	0.0482978	−	0.0207310i
$261$	−5.32131e39			−0.710314
$262$			4.81502e39i			0.603429i
$263$			2.81811e39i			0.331656i	0.986155	+	0.165828i	$0.0530296\pi$
$263$			2.81811e39i			0.331656i	−0.986155	+	0.165828i	$0.946970\pi$
$264$	−2.91749e39			−0.322511
$265$	9.17265e39	−	3.93721e39i	0.952660	−	0.408913i
$266$	−2.56110e39			−0.249965
$267$		−	4.12398e39i		−	0.378338i
$268$			1.08849e40i			0.938857i
$269$	1.58985e40			1.28956			0.644781	−	0.764367i	$-0.276948\pi$
$269$	1.58985e40			1.28956			0.644781	+	0.764367i	$0.276948\pi$
$270$	2.75651e39	+	6.42194e39i	0.210309	+	0.489964i
$271$	−1.95396e40			−1.40256			−0.701281	−	0.712885i	$-0.747388\pi$
$271$	−1.95396e40			−1.40256			−0.701281	+	0.712885i	$0.747388\pi$
$272$		−	2.66986e38i		−	0.0180344i
$273$		−	1.53238e38i		−	0.00974275i
$274$	2.03855e40			1.22022
$275$	8.67711e39	−	9.13138e39i	0.489086	−	0.514692i
$276$	1.07353e39			0.0569922
$277$		−	3.35857e40i		−	1.67973i	−0.542799	−	0.839863i	$-0.682635\pi$
$277$		−	3.35857e40i		−	1.67973i	0.542799	−	0.839863i	$-0.317365\pi$
$278$			6.67399e39i			0.314519i
$279$	−4.24146e39			−0.188385
$280$	−2.26998e39	−	5.28845e39i	−0.0950418	−	0.221422i
$281$	−3.53786e40			−1.39665			−0.698323	−	0.715783i	$-0.746070\pi$
$281$	−3.53786e40			−1.39665			−0.698323	+	0.715783i	$0.746070\pi$
$282$			6.23011e39i			0.231945i
$283$		−	3.47855e40i		−	1.22158i	−0.791793	−	0.610790i	$-0.790852\pi$
$283$		−	3.47855e40i		−	1.22158i	0.791793	−	0.610790i	$-0.209148\pi$
$284$	−1.60723e40			−0.532508
$285$	2.04730e40	−	8.78771e39i	0.640091	−	0.274749i
$286$	−1.57728e39			−0.0465447
$287$		−	1.06935e40i		−	0.297900i
$288$			2.87413e40i			0.756016i
$289$	3.97645e40			0.987828
$290$	2.32175e40	−	9.96572e39i	0.544814	−	0.233852i
$291$	5.98389e39			0.132663
$292$		−	1.47557e39i		−	0.0309130i
$293$			1.96947e40i			0.389973i	0.980806	+	0.194986i	$0.0624663\pi$
$293$			1.96947e40i			0.389973i	−0.980806	+	0.194986i	$0.937534\pi$
$294$	1.48943e40			0.278798
$295$	1.22692e40	+	2.85839e40i	0.217146	+	0.505892i
$296$	−9.88989e40			−1.65531
$297$			3.53487e40i			0.559618i
$298$			2.29781e38i			0.00344149i
$299$	1.65047e39			0.0233901
$300$	1.27619e40	+	1.21270e40i	0.171165	+	0.162650i
$301$	−2.04446e40			−0.259556
$302$			3.54162e40i			0.425684i
$303$			3.43912e40i			0.391421i
$304$	−2.42637e40			−0.261543
$305$	3.06348e40	+	7.13709e40i	0.312800	+	0.728742i
$306$	−6.25295e39			−0.0604897
$307$			1.02313e40i			0.0937882i	0.998900	+	0.0468941i	$0.0149323\pi$
$307$			1.02313e40i			0.0937882i	−0.998900	+	0.0468941i	$0.985068\pi$
$308$		−	1.02363e40i		−	0.0889317i
$309$	−8.39942e40			−0.691726
$310$	1.85060e40	−	7.94338e39i	0.144492	−	0.0620208i
$311$	−1.63827e40			−0.121294			−0.0606469	−	0.998159i	$-0.519316\pi$
$311$	−1.63827e40			−0.121294			−0.0606469	+	0.998159i	$0.519316\pi$
$312$		−	6.26877e39i		−	0.0440181i
$313$		−	2.45388e41i		−	1.63445i	−0.576319	−	0.817225i	$-0.695511\pi$
$313$		−	2.45388e41i		−	1.63445i	0.576319	−	0.817225i	$-0.304489\pi$
$314$	6.98732e38			0.00441541
$315$	−2.86839e40	+	1.23121e40i	−0.171994	+	0.0738257i
$316$	7.24482e40			0.412279
$317$			9.53656e40i			0.515127i	0.966261	+	0.257563i	$0.0829196\pi$
$317$			9.53656e40i			0.515127i	−0.966261	+	0.257563i	$0.917080\pi$
$318$		−	5.95385e40i		−	0.305316i
$319$	1.27797e41			0.622265
$320$	−6.77698e40	−	1.57886e41i	−0.313373	−	0.730077i
$321$	4.06778e40			0.178659
$322$		−	9.03768e39i		−	0.0377081i
$323$			4.45302e40i			0.176528i
$324$	6.72855e40			0.253471
$325$	1.96204e40	+	1.86444e40i	0.0702479	+	0.0667532i
$326$	1.83213e41			0.623543
$327$			1.57554e40i			0.0509789i
$328$		−	4.37460e41i		−	1.34592i
$329$	−6.21614e40			−0.181882
$330$	−2.96353e40	−	6.90424e40i	−0.0824764	−	0.192148i
$331$	3.20466e41			0.848439			0.424219	−	0.905559i	$-0.360549\pi$
$331$	3.20466e41			0.848439			0.424219	+	0.905559i	$0.360549\pi$
$332$		−	2.76296e41i		−	0.695980i
$333$			5.36415e41i			1.28579i
$334$	2.25295e41			0.513967
$335$	−7.32524e41	+	3.14424e41i	−1.59068	+	0.682772i
$336$	−7.94961e39			−0.0164342
$337$		−	3.99673e41i		−	0.786704i	−0.919388	−	0.393352i	$-0.871315\pi$
$337$		−	3.99673e41i		−	0.786704i	0.919388	−	0.393352i	$-0.128685\pi$
$338$			3.57507e41i			0.670130i
$339$	−3.87245e41			−0.691338
$340$	−3.23344e40	+	1.38790e40i	−0.0549874	+	0.0236024i
$341$	1.01864e41			0.165033
$342$			5.68267e41i			0.877246i
$343$			3.05591e41i			0.449560i
$344$	−8.36364e41			−1.17268
$345$	3.10103e40	+	7.22459e40i	0.0414469	+	0.0965602i
$346$	1.04703e42			1.33415
$347$			2.95633e41i			0.359183i	0.983741	+	0.179592i	$0.0574776\pi$
$347$			2.95633e41i			0.359183i	−0.983741	+	0.179592i	$0.942522\pi$
$348$			1.78608e41i			0.206940i
$349$	−9.02618e41			−0.997434			−0.498717	−	0.866765i	$-0.666195\pi$
$349$	−9.02618e41			−0.997434			−0.498717	+	0.866765i	$0.666195\pi$
$350$	1.02093e41	−	1.07438e41i	0.107615	−	0.113249i
$351$	−7.59531e40			−0.0763797
$352$		−	6.90256e41i		−	0.662302i
$353$			1.20764e42i			1.10575i	0.833265	+	0.552874i	$0.186469\pi$
$353$			1.20764e42i			1.10575i	−0.833265	+	0.552874i	$0.813531\pi$
$354$	1.85534e41			0.162133
$355$	−4.64270e41	−	1.08163e42i	−0.387260	−	0.902214i
$356$	5.91925e41			0.471348
$357$			1.45896e40i			0.0110922i
$358$		−	1.44583e42i		−	1.04965i
$359$	1.37495e42			0.953299			0.476649	−	0.879093i	$-0.341851\pi$
$359$	1.37495e42			0.953299			0.476649	+	0.879093i	$0.341851\pi$
$360$	−1.17342e42	+	5.03673e41i	−0.777077	+	0.333547i
$361$	2.46612e42			1.56008
$362$			1.56437e42i			0.945473i
$363$			3.73833e41i			0.215883i
$364$	2.19946e40			0.0121379
$365$	9.93017e40	−	4.26236e40i	0.0523751	−	0.0224811i
$366$	4.63260e41			0.233554
$367$		−	3.82875e42i		−	1.84530i	−0.385637	−	0.922651i	$-0.626018\pi$
$367$		−	3.82875e42i		−	1.84530i	0.385637	−	0.922651i	$-0.373982\pi$
$368$		−	8.56224e40i		−	0.0394547i
$369$	−2.37273e42			−1.04547
$370$	−1.00460e42	−	2.34044e42i	−0.423314	−	0.986210i
$371$	5.94050e41			0.239416
$372$			1.42364e41i			0.0548833i
$373$		−	2.86200e42i		−	1.05554i	−0.849387	−	0.527770i	$-0.823028\pi$
$373$		−	2.86200e42i		−	1.05554i	0.849387	−	0.527770i	$-0.176972\pi$
$374$	1.50172e41			0.0529916
$375$	−4.47474e41	+	1.20915e42i	−0.151096	+	0.408286i
$376$	−2.54295e42			−0.821747
$377$			2.74596e41i			0.0849302i
$378$			4.15906e41i			0.123135i
$379$	2.49740e42			0.707849			0.353925	−	0.935274i	$-0.384847\pi$
$379$	2.49740e42			0.707849			0.353925	+	0.935274i	$0.384847\pi$
$380$	1.26132e42	+	2.93855e42i	0.342292	+	0.797449i
$381$	1.05319e42			0.273681
$382$			4.13790e42i			1.02976i
$383$			4.91079e41i			0.117050i	0.998286	+	0.0585250i	$0.0186397\pi$
$383$			4.91079e41i			0.117050i	−0.998286	+	0.0585250i	$0.981360\pi$
$384$	7.53845e41			0.172114
$385$	6.88877e41	−	2.95689e41i	0.150674	−	0.0646745i
$386$	−3.33792e42			−0.699496
$387$			4.53633e42i			0.910906i
$388$			8.58883e41i			0.165276i
$389$	−5.44420e41			−0.100407			−0.0502037	−	0.998739i	$-0.515987\pi$
$389$	−5.44420e41			−0.100407			−0.0502037	+	0.998739i	$0.515987\pi$
$390$	1.48350e41	−	6.36769e40i	0.0262254	−	0.0112568i
$391$	−1.57139e41			−0.0266299
$392$			6.07943e42i			0.987741i
$393$		−	2.49277e42i		−	0.388334i
$394$	−3.88686e41			−0.0580645
$395$	2.09276e42	+	4.87558e42i	0.299825	+	0.698512i
$396$	−2.27128e42			−0.312104
$397$		−	1.16147e43i		−	1.53096i	−0.643459	−	0.765481i	$-0.722501\pi$
$397$		−	1.16147e43i		−	1.53096i	0.643459	−	0.765481i	$-0.277499\pi$
$398$		−	1.33670e42i		−	0.169030i
$399$	1.32590e42			0.160864
$400$	9.67225e41	−	1.01786e42i	0.112600	−	0.118495i
$401$	−1.02132e43			−1.14098			−0.570492	−	0.821303i	$-0.693247\pi$
$401$	−1.02132e43			−1.14098			−0.570492	+	0.821303i	$0.693247\pi$
$402$			4.75472e42i			0.509794i
$403$			2.18873e41i			0.0225246i
$404$	−4.93626e42			−0.487647
$405$	1.94363e42	+	4.52814e42i	0.184334	+	0.429449i
$406$	1.50364e42			0.136919
$407$		−	1.28826e43i		−	1.12641i
$408$			5.96843e41i			0.0501150i
$409$	8.75689e42			0.706180			0.353090	−	0.935589i	$-0.385131\pi$
$409$	8.75689e42			0.706180			0.353090	+	0.935589i	$0.385131\pi$
$410$	1.03525e43	−	4.44363e42i	0.801883	−	0.344195i
$411$	−1.05537e43			−0.785265
$412$		−	1.20559e43i		−	0.861778i
$413$			1.85119e42i			0.127138i
$414$	−2.00532e42			−0.132336
$415$	1.85940e43	−	7.98117e42i	1.17918	−	0.506143i
$416$	1.48314e42			0.0903946
$417$		−	3.45518e42i		−	0.202407i
$418$		−	1.36476e43i		−	0.768505i
$419$	8.87775e42			0.480586			0.240293	−	0.970700i	$-0.422756\pi$
$419$	8.87775e42			0.480586			0.240293	+	0.970700i	$0.422756\pi$
$420$	4.13252e41	+	9.62768e41i	0.0215081	+	0.0501081i
$421$	−9.76948e42			−0.488897			−0.244448	−	0.969662i	$-0.578607\pi$
$421$	−9.76948e42			−0.488897			−0.244448	+	0.969662i	$0.578607\pi$
$422$			2.16646e43i			1.04255i
$423$			1.37926e43i			0.638309i
$424$	2.43019e43			1.08169
$425$	−1.86804e42	−	1.77511e42i	−0.0799778	−	0.0759990i
$426$	−7.02070e42			−0.289149
$427$			4.62221e42i			0.183143i
$428$			5.83859e42i			0.222580i
$429$	8.16573e41			0.0299537
$430$	−8.49561e42	−	1.97925e43i	−0.299892	−	0.698669i
$431$	−5.70318e43			−1.93750			−0.968751	−	0.248034i	$-0.920215\pi$
$431$	−5.70318e43			−1.93750			−0.968751	+	0.248034i	$0.920215\pi$
$432$			3.94027e42i			0.128838i
$433$			2.71186e43i			0.853528i	0.904363	+	0.426764i	$0.140346\pi$
$433$			2.71186e43i			0.853528i	−0.904363	+	0.426764i	$0.859654\pi$
$434$	1.19851e42			0.0363128
$435$	−1.20199e43	+	5.15933e42i	−0.350613	+	0.150495i
$436$	−2.26141e42			−0.0635114
$437$			1.42808e43i			0.386197i
$438$		−	6.44555e41i		−	0.0167856i
$439$	−3.17561e43			−0.796457			−0.398228	−	0.917286i	$-0.630375\pi$
$439$	−3.17561e43			−0.796457			−0.398228	+	0.917286i	$0.630375\pi$
$440$	2.81811e43	−	1.20963e43i	0.680753	−	0.292202i
$441$	3.29741e43			0.767248
$442$			3.22671e41i			0.00723257i
$443$			4.05139e43i			0.874868i	0.899250	+	0.437434i	$0.144113\pi$
$443$			4.05139e43i			0.874868i	−0.899250	+	0.437434i	$0.855887\pi$
$444$	1.80046e43			0.374598
$445$	1.70985e43	+	3.98350e43i	0.342782	+	0.798591i
$446$	−4.71961e43			−0.911761
$447$		−	1.18960e41i		−	0.00221475i
$448$		−	1.02252e43i		−	0.183478i
$449$	1.03840e43			0.179598			0.0897989	−	0.995960i	$-0.471378\pi$
$449$	1.03840e43			0.179598			0.0897989	+	0.995960i	$0.471378\pi$
$450$	−2.38388e43	−	2.26529e43i	−0.397446	−	0.377674i
$451$	5.69838e43			0.915880
$452$		−	5.55822e43i		−	0.861294i
$453$		−	1.83352e43i		−	0.273947i
$454$	−5.50101e43			−0.792540
$455$	6.35342e41	+	1.48018e42i	0.00882712	+	0.0205649i
$456$	5.42410e43			0.726788
$457$			2.54691e43i			0.329152i	0.986364	+	0.164576i	$0.0526255\pi$
$457$			2.54691e43i			0.329152i	−0.986364	+	0.164576i	$0.947374\pi$
$458$		−	6.57595e43i		−	0.819744i
$459$	7.23142e42			0.0869589
$460$	−1.03696e43	+	4.45099e42i	−0.120298	+	0.0516360i
$461$	6.21946e43			0.696126			0.348063	−	0.937471i	$-0.386840\pi$
$461$	6.21946e43			0.696126			0.348063	+	0.937471i	$0.386840\pi$
$462$		−	4.47141e42i		−	0.0482894i
$463$		−	8.30551e43i		−	0.865525i	−0.901508	−	0.432763i	$-0.857539\pi$
$463$		−	8.30551e43i		−	0.865525i	0.901508	−	0.432763i	$-0.142461\pi$
$464$	1.42454e43			0.143261
$465$	−9.58070e42	+	4.11235e42i	−0.0929873	+	0.0399132i
$466$	6.11318e43			0.572664
$467$		−	4.20816e43i		−	0.380508i	−0.981735	−	0.190254i	$-0.939069\pi$
$467$		−	4.20816e43i		−	0.380508i	0.981735	−	0.190254i	$-0.0609311\pi$
$468$		−	4.88025e42i		−	0.0425976i
$469$	−4.74406e43			−0.399759
$470$	−2.58308e43	−	6.01789e43i	−0.210147	−	0.489586i
$471$	−3.61739e41			−0.00284152
$472$			7.57298e43i			0.574412i
$473$		−	1.08945e44i		−	0.797993i
$474$	3.16467e43			0.223865
$475$	−1.61322e44	+	1.69767e44i	−1.10217	+	1.15987i
$476$	−2.09408e42			−0.0138191
$477$		−	1.31810e44i		−	0.840227i
$478$			1.40191e44i			0.863295i
$479$	−7.24792e43			−0.431199			−0.215599	−	0.976482i	$-0.569171\pi$
$479$	−7.24792e43			−0.431199			−0.215599	+	0.976482i	$0.569171\pi$
$480$	2.78665e43	+	6.49215e43i	0.160177	+	0.373171i
$481$	2.76807e43			0.153739
$482$			5.08869e43i			0.273105i
$483$			4.67888e42i			0.0242669i
$484$	−5.36572e43			−0.268955
$485$	−5.78006e43	+	2.48099e43i	−0.280023	+	0.120195i
$486$	1.43255e44			0.670826
$487$			1.88889e44i			0.855023i	0.904010	+	0.427512i	$0.140610\pi$
$487$			1.88889e44i			0.855023i	−0.904010	+	0.427512i	$0.859390\pi$
$488$			1.89089e44i			0.827446i
$489$	−9.48509e43			−0.401278
$490$	−1.43870e44	+	6.17536e43i	−0.588483	+	0.252596i
$491$	4.17277e44			1.65036			0.825182	−	0.564867i	$-0.191073\pi$
$491$	4.17277e44			1.65036			0.825182	+	0.564867i	$0.191073\pi$
$492$			7.96400e43i			0.304584i
$493$		−	2.61440e43i		−	0.0966937i
$494$	2.93243e43			0.104890
$495$	−6.56087e43	−	1.52851e44i	−0.226974	−	0.528789i
$496$	1.13546e43			0.0379948
$497$		−	7.00496e43i		−	0.226738i
$498$		−	1.20691e44i		−	0.377913i
$499$	−2.81200e43			−0.0851838			−0.0425919	−	0.999093i	$-0.513562\pi$
$499$	−2.81200e43			−0.0851838			−0.0425919	+	0.999093i	$0.513562\pi$
$500$	−1.73552e44	−	6.42270e43i	−0.508657	−	0.188240i
$501$	−1.16637e44			−0.330761
$502$			1.93609e44i			0.531267i
$503$			7.45270e43i			0.197898i	0.995092	+	0.0989491i	$0.0315481\pi$
$503$			7.45270e43i			0.197898i	−0.995092	+	0.0989491i	$0.968452\pi$
$504$	−7.59948e43			−0.195290
$505$	−1.42590e44	−	3.32197e44i	−0.354635	−	0.826206i
$506$	4.81600e43			0.115932
$507$		−	1.85084e44i		−	0.431259i
$508$			1.51167e44i			0.340962i
$509$	4.47746e44			0.977661			0.488831	−	0.872379i	$-0.337424\pi$
$509$	4.47746e44			0.977661			0.488831	+	0.872379i	$0.337424\pi$
$510$	−1.41243e43	+	6.06261e42i	−0.0298578	+	0.0128160i
$511$	6.43110e42			0.0131626
$512$		−	1.63005e44i		−	0.323032i
$513$		−	6.57190e44i		−	1.26111i
$514$	−4.62155e44			−0.858809
$515$	8.11330e44	−	3.48250e44i	1.46009	−	0.626717i
$516$	1.52261e44			0.265380
$517$		−	3.31246e44i		−	0.559187i
$518$		−	1.51575e44i		−	0.247848i
$519$	−5.42056e44			−0.858585
$520$	2.59911e43	+	6.05523e43i	0.0398813	+	0.0929128i
$521$	6.18290e43			0.0919115			0.0459558	−	0.998943i	$-0.485367\pi$
$521$	6.18290e43			0.0919115			0.0459558	+	0.998943i	$0.485367\pi$
$522$		−	3.33634e44i		−	0.480515i
$523$			1.40874e45i			1.96586i	0.183989	+	0.982928i	$0.441099\pi$
$523$			1.40874e45i			1.96586i	−0.183989	+	0.982928i	$0.558901\pi$
$524$	3.57794e44			0.483801
$525$	−5.28545e43	+	5.56216e43i	−0.0692553	+	0.0728811i
$526$	−1.76689e44			−0.224359
$527$		−	2.08386e43i		−	0.0256445i
$528$		−	4.23619e43i		−	0.0505261i
$529$	8.14610e44			0.941741
$530$	2.46854e44	+	5.75104e44i	0.276623	+	0.644458i
$531$	4.10749e44			0.446187
$532$			1.90310e44i			0.200410i
$533$			1.22440e44i			0.125004i
$534$	2.58564e44			0.255939
$535$	−3.92922e44	+	1.68655e44i	−0.377111	+	0.161868i
$536$	−1.94074e45			−1.80613
$537$			7.48516e44i			0.675500i
$538$			9.96797e44i			0.872367i
$539$	−7.91910e44			−0.672143
$540$	4.77201e44	−	2.04831e44i	0.392830	−	0.168616i
$541$	−1.33014e45			−1.06205			−0.531023	−	0.847357i	$-0.678192\pi$
$541$	−1.33014e45			−1.06205			−0.531023	+	0.847357i	$0.678192\pi$
$542$		−	1.22509e45i		−	0.948808i
$543$		−	8.09889e44i		−	0.608455i
$544$	−1.41208e44			−0.102915
$545$	−6.53236e43	−	1.52187e44i	−0.0461879	−	0.107606i
$546$	9.60764e42			0.00659080
$547$			2.40170e45i			1.59856i	0.600961	+	0.799279i	$0.294785\pi$
$547$			2.40170e45i			1.59856i	−0.600961	+	0.799279i	$0.705215\pi$
$548$		−	1.51480e45i		−	0.978312i
$549$	1.02560e45			0.642736
$550$	5.72516e44	+	5.44034e44i	0.348180	+	0.330858i
$551$	−2.37596e45			−1.40229
$552$			1.91407e44i			0.109639i
$553$			3.15758e44i			0.175546i
$554$	2.10575e45			1.13631
$555$	5.20087e44	+	1.21167e45i	0.272422	+	0.634671i
$556$	4.95931e44			0.252166
$557$		−	5.78171e44i		−	0.285394i	−0.989766	−	0.142697i	$-0.954422\pi$
$557$		−	5.78171e44i		−	0.285394i	0.989766	−	0.142697i	$-0.0455775\pi$
$558$		−	2.65930e44i		−	0.127439i
$559$	2.34089e44			0.108914
$560$	7.67882e43	−	3.29600e43i	0.0346890	−	0.0148897i
$561$	−7.77451e43			−0.0341025
$562$		−	2.21816e45i		−	0.944807i
$563$		−	9.78977e44i		−	0.404934i	−0.979289	−	0.202467i	$-0.935104\pi$
$563$		−	9.78977e44i		−	0.404934i	0.979289	−	0.202467i	$-0.0648959\pi$
$564$	4.62946e44			0.185963
$565$	3.74054e45	−	1.60556e45i	1.45927	−	0.626365i
$566$	2.18097e45			0.826378
$567$			2.93257e44i			0.107926i
$568$		−	2.86565e45i		−	1.02441i
$569$	−2.73187e45			−0.948654			−0.474327	−	0.880349i	$-0.657309\pi$
$569$	−2.73187e45			−0.948654			−0.474327	+	0.880349i	$0.657309\pi$
$570$	5.50969e44	+	1.28361e45i	0.185863	+	0.433011i
$571$	−3.69219e45			−1.21001			−0.605004	−	0.796222i	$-0.706829\pi$
$571$	−3.69219e45			−1.21001			−0.605004	+	0.796222i	$0.706829\pi$
$572$			1.17205e44i			0.0373174i
$573$		−	2.14222e45i		−	0.662695i
$574$	6.70461e44			0.201524
$575$	−5.99081e44	−	5.69277e44i	−0.174971	−	0.166266i
$576$	−2.26881e45			−0.643913
$577$		−	6.65464e44i		−	0.183537i	−0.995780	−	0.0917685i	$-0.970748\pi$
$577$		−	6.65464e44i		−	0.183537i	0.995780	−	0.0917685i	$-0.0292520\pi$
$578$			2.49314e45i			0.668248i
$579$	1.72807e45			0.450157
$580$	−7.40532e44	−	1.72524e45i	−0.187492	−	0.436806i
$581$	1.20421e45			0.296344
$582$			3.75176e44i			0.0897441i
$583$			3.16558e45i			0.736075i
$584$	2.63089e44			0.0594689
$585$	3.28428e44	−	1.40972e44i	0.0721720	−	0.0309786i
$586$	−1.23481e45			−0.263810
$587$			7.63092e45i			1.58507i	0.609827	+	0.792535i	$0.291239\pi$
$587$			7.63092e45i			1.58507i	−0.609827	+	0.792535i	$0.708761\pi$
$588$		−	1.10677e45i		−	0.223527i
$589$	−1.89381e45			−0.371907
$590$	−1.79214e45	+	7.69248e44i	−0.342227	+	0.146895i
$591$	2.01226e44			0.0373672
$592$		−	1.43601e45i		−	0.259328i
$593$			1.35734e45i			0.238388i	0.992871	+	0.119194i	$0.0380311\pi$
$593$			1.35734e45i			0.238388i	−0.992871	+	0.119194i	$0.961969\pi$
$594$	−2.21628e45			−0.378572
$595$	−6.04902e43	−	1.40926e44i	−0.0100498	−	0.0234133i
$596$	1.70746e43			0.00275922
$597$			6.92022e44i			0.108779i
$598$			1.03481e44i			0.0158230i
$599$	−2.59608e45			−0.386167			−0.193083	−	0.981182i	$-0.561849\pi$
$599$	−2.59608e45			−0.386167			−0.193083	+	0.981182i	$0.561849\pi$
$600$	−2.16221e45	+	2.27541e45i	−0.312898	+	0.329279i
$601$	1.37129e46			1.93063			0.965316	−	0.261086i	$-0.0840807\pi$
$601$	1.37129e46			1.93063			0.965316	+	0.261086i	$0.0840807\pi$
$602$		−	1.28183e45i		−	0.175585i
$603$			1.05263e46i			1.40295i
$604$	2.63170e45			0.341293
$605$	−1.54996e45	−	3.61099e45i	−0.195594	−	0.455683i
$606$	−2.15625e45			−0.264789
$607$		−	6.01305e45i		−	0.718590i	−0.933224	−	0.359295i	$-0.883017\pi$
$607$		−	6.01305e45i		−	0.718590i	0.933224	−	0.359295i	$-0.116983\pi$
$608$			1.28330e46i			1.49252i
$609$	−7.78446e44			−0.0881137
$610$	−4.47479e45	+	1.92073e45i	−0.492981	+	0.211604i
$611$	7.11743e44			0.0763208
$612$			4.64644e44i			0.0484977i
$613$		−	1.58173e46i		−	1.60707i	−0.595260	−	0.803533i	$-0.702951\pi$
$613$		−	1.58173e46i		−	1.60707i	0.595260	−	0.803533i	$-0.297049\pi$
$614$	−6.41479e44			−0.0634460
$615$	−5.35957e45	+	2.30050e45i	−0.516048	+	0.221505i
$616$	1.82510e45			0.171082
$617$		−	2.03656e46i		−	1.85863i	−0.369294	−	0.929313i	$-0.620400\pi$
$617$		−	2.03656e46i		−	1.85863i	0.369294	−	0.929313i	$-0.379600\pi$
$618$		−	5.26624e45i		−	0.467941i
$619$	3.14597e45			0.272181			0.136091	−	0.990696i	$-0.456546\pi$
$619$	3.14597e45			0.272181			0.136091	+	0.990696i	$0.456546\pi$
$620$	−5.90257e44	−	1.37514e45i	−0.0497254	−	0.115847i
$621$	2.31911e45			0.190244
$622$		−	1.02716e45i		−	0.0820531i
$623$			2.57984e45i			0.200697i
$624$	9.10223e43			0.00689607
$625$	−6.90970e44	−	1.35349e46i	−0.0509846	−	0.998699i
$626$	1.53853e46			1.10568
$627$			7.06546e45i			0.494568i
$628$		−	5.19213e43i		−	0.00354007i
$629$	−2.63545e45			−0.175033
$630$	−7.71939e44	−	1.79841e45i	−0.0499418	−	0.116351i
$631$	1.08624e46			0.684607			0.342303	−	0.939589i	$-0.388793\pi$
$631$	1.08624e46			0.684607			0.342303	+	0.939589i	$0.388793\pi$
$632$			1.29173e46i			0.793121i
$633$		−	1.12160e46i		−	0.670927i
$634$	−5.97920e45			−0.348474
$635$	−1.01732e46	+	4.36665e45i	−0.577682	+	0.247960i
$636$	−4.42418e45			−0.244788
$637$		−	1.70156e45i		−	0.0917377i
$638$			8.01260e45i			0.420952i
$639$	−1.55429e46			−0.795734
$640$	−7.28167e45	+	3.12553e45i	−0.363297	+	0.155939i
$641$	3.22979e46			1.57042			0.785211	−	0.619228i	$-0.212554\pi$
$641$	3.22979e46			1.57042			0.785211	+	0.619228i	$0.212554\pi$
$642$			2.55041e45i			0.120860i
$643$		−	1.51385e46i		−	0.699201i	−0.936899	−	0.349600i	$-0.886317\pi$
$643$		−	1.51385e46i		−	0.699201i	0.936899	−	0.349600i	$-0.113683\pi$
$644$	−6.71571e44			−0.0302326
$645$	4.39825e45	+	1.02468e46i	0.192994	+	0.449626i
$646$	−2.79194e45			−0.119418
$647$			3.60709e46i			1.50396i	0.659185	+	0.751981i	$0.270901\pi$
$647$			3.60709e46i			1.50396i	−0.659185	+	0.751981i	$0.729099\pi$
$648$			1.19968e46i			0.487616i
$649$	−9.86460e45			−0.390879
$650$	−1.16896e45	+	1.23016e45i	−0.0451573	+	0.0475215i
$651$	−6.20477e44			−0.0233690
$652$		−	1.36142e46i		−	0.499927i
$653$		−	9.59570e44i		−	0.0343565i	−0.999852	−	0.0171783i	$-0.994532\pi$
$653$		−	9.59570e44i		−	0.0343565i	0.999852	−	0.0171783i	$-0.00546828\pi$
$654$	−9.87825e44			−0.0344863
$655$	1.03353e46	+	2.40786e46i	0.351838	+	0.819690i
$656$	6.35191e45			0.210858
$657$		−	1.42696e45i		−	0.0461937i
$658$		−	3.89738e45i		−	0.123040i
$659$	−3.45120e46			−1.06258			−0.531289	−	0.847191i	$-0.678292\pi$
$659$	−3.45120e46			−1.06258			−0.531289	+	0.847191i	$0.678292\pi$
$660$	−5.13040e45	+	2.20214e45i	−0.154055	+	0.0661256i
$661$	−3.13661e46			−0.918622			−0.459311	−	0.888276i	$-0.651904\pi$
$661$	−3.13661e46			−0.918622			−0.459311	+	0.888276i	$0.651904\pi$
$662$			2.00925e46i			0.573954i
$663$		−	1.67050e44i		−	0.00465449i
$664$	4.92627e46			1.33889
$665$	−1.28073e46	+	5.49734e45i	−0.339549	+	0.145746i
$666$	−3.36320e46			−0.869817
$667$		−	8.38437e45i		−	0.211541i
$668$		−	1.67412e46i		−	0.412074i
$669$	2.44338e46			0.586760
$670$	−1.97136e46	−	4.59276e46i	−0.461884	−	1.07607i
$671$	−2.46309e46			−0.563064
$672$			4.20453e45i			0.0937830i
$673$		−	2.02753e46i		−	0.441284i	−0.975355	−	0.220642i	$-0.929185\pi$
$673$		−	2.02753e46i		−	0.441284i	0.975355	−	0.220642i	$-0.0708152\pi$
$674$	2.50586e46			0.532191
$675$	2.75691e46	+	2.61976e46i	0.571361	+	0.542937i
$676$	2.65656e46			0.537278
$677$		−	6.36048e46i		−	1.25539i	−0.778461	−	0.627693i	$-0.783999\pi$
$677$		−	6.36048e46i		−	1.25539i	0.778461	−	0.627693i	$-0.216001\pi$
$678$		−	2.42793e46i		−	0.467678i
$679$	−3.74335e45			−0.0703736
$680$	−2.47458e45	−	5.76513e45i	−0.0454051	−	0.105782i
$681$	2.84792e46			0.510036
$682$			6.38661e45i			0.111642i
$683$			5.99654e46i			1.02320i	0.859225	+	0.511599i	$0.170946\pi$
$683$			5.99654e46i			1.02320i	−0.859225	+	0.511599i	$0.829054\pi$
$684$	4.22267e46			0.703334
$685$	1.01942e47	−	4.37571e46i	1.65753	−	0.711465i
$686$	−1.91598e46			−0.304119
$687$			3.40442e46i			0.527542i
$688$		−	1.21440e46i		−	0.183718i
$689$	−6.80182e45			−0.100463
$690$	−4.52965e45	+	1.94428e45i	−0.0653213	+	0.0280381i
$691$	−5.59226e46			−0.787407			−0.393704	−	0.919237i	$-0.628806\pi$
$691$	−5.59226e46			−0.787407			−0.393704	+	0.919237i	$0.628806\pi$
$692$		−	7.78027e46i		−	1.06966i
$693$		−	9.89912e45i		−	0.132892i
$694$	−1.85355e46			−0.242981
$695$	1.43256e46	+	3.33748e46i	0.183385	+	0.427238i
$696$	−3.18453e46			−0.398101
$697$		−	1.16574e46i		−	0.142318i
$698$		−	5.65920e46i		−	0.674747i
$699$	−3.16485e46			−0.368535
$700$	−7.98350e45	−	7.58633e45i	−0.0907979	−	0.0862808i
$701$	−1.24770e47			−1.38600			−0.692999	−	0.720938i	$-0.743711\pi$
$701$	−1.24770e47			−1.38600			−0.692999	+	0.720938i	$0.743711\pi$
$702$		−	4.76208e45i		−	0.0516695i
$703$			2.39509e47i			2.53840i
$704$	5.44881e46			0.564095
$705$	1.33728e46	+	3.11551e46i	0.135239	+	0.315071i
$706$	−7.57165e46			−0.748019
$707$		−	2.15142e46i		−	0.207637i
$708$		−	1.37867e46i		−	0.129990i
$709$	−2.48163e46			−0.228599			−0.114300	−	0.993446i	$-0.536462\pi$
$709$	−2.48163e46			−0.228599			−0.114300	+	0.993446i	$0.536462\pi$
$710$	6.78155e46	−	2.91086e46i	0.610332	−	0.261975i
$711$	7.00617e46			0.616073
$712$			1.05538e47i			0.906755i
$713$		−	6.68294e45i		−	0.0561036i
$714$	−9.14734e44			−0.00750368
$715$	−7.88758e45	+	3.38561e45i	−0.0632257	+	0.0271386i
$716$	−1.07436e47			−0.841563
$717$		−	7.25779e46i		−	0.555569i
$718$			8.62063e46i			0.644890i
$719$	−7.59986e46			−0.555621			−0.277811	−	0.960636i	$-0.589609\pi$
$719$	−7.59986e46			−0.555621			−0.277811	+	0.960636i	$0.589609\pi$
$720$	−7.31331e45	−	1.70381e46i	−0.0522550	−	0.121740i
$721$	5.25444e46			0.366939
$722$			1.54620e47i			1.05536i
$723$		−	2.63446e46i		−	0.175756i
$724$	1.16245e47			0.758035
$725$	9.47132e46	−	9.96717e46i	0.603717	−	0.635324i
$726$	−2.34385e46			−0.146041
$727$			1.84497e47i			1.12376i	0.827220	+	0.561879i	$0.189921\pi$
$727$			1.84497e47i			1.12376i	−0.827220	+	0.561879i	$0.810079\pi$
$728$			3.92156e45i			0.0233502i
$729$	6.12127e45			0.0356318
$730$	2.67240e45	+	6.22599e45i	0.0152081	+	0.0354308i
$731$	−2.22873e46			−0.124000
$732$		−	3.44239e46i		−	0.187252i
$733$		−	1.24110e47i		−	0.660071i	−0.943969	−	0.330035i	$-0.892939\pi$
$733$		−	1.24110e47i		−	0.660071i	0.943969	−	0.330035i	$-0.107061\pi$
$734$	2.40054e47			1.24831
$735$	7.44825e46	−	3.19704e46i	0.378716	−	0.162557i
$736$	−4.52855e46			−0.225152
$737$		−	2.52802e47i		−	1.22904i
$738$		−	1.48765e47i		−	0.707245i
$739$	−1.88241e47			−0.875146			−0.437573	−	0.899183i	$-0.644162\pi$
$739$	−1.88241e47			−0.875146			−0.437573	+	0.899183i	$0.644162\pi$
$740$	−1.73913e47	+	7.46494e46i	−0.790696	+	0.339393i
$741$	−1.51814e46			−0.0675013
$742$			3.72456e46i			0.161961i
$743$		−	2.41383e47i		−	1.02657i	−0.858217	−	0.513287i	$-0.828428\pi$
$743$		−	2.41383e47i		−	1.02657i	0.858217	−	0.513287i	$-0.171572\pi$
$744$	−2.53830e46			−0.105582
$745$	4.93221e44	+	1.14907e45i	0.00200661	+	0.00467487i
$746$	1.79441e47			0.714054
$747$		−	2.67195e47i		−	1.04001i
$748$		−	1.11589e46i		−	0.0424861i
$749$	−2.54469e46			−0.0947730
$750$	−7.58109e46	−	2.80556e46i	−0.276198	−	0.102213i
$751$	2.35425e46			0.0839062			0.0419531	−	0.999120i	$-0.486642\pi$
$751$	2.35425e46			0.0839062			0.0419531	+	0.999120i	$0.486642\pi$
$752$		−	3.69235e46i		−	0.128739i
$753$		−	1.00233e47i		−	0.341895i
$754$	−1.72165e46			−0.0574538
$755$	7.60201e46	+	1.77107e47i	0.248201	+	0.578243i
$756$	3.09051e46			0.0987235
$757$			2.42635e47i			0.758354i	0.925324	+	0.379177i	$0.123793\pi$
$757$			2.42635e47i			0.758354i	−0.925324	+	0.379177i	$0.876207\pi$
$758$			1.56581e47i			0.478847i
$759$	−2.49328e46			−0.0746075
$760$	−5.23933e47	+	2.24890e47i	−1.53409	+	0.658484i
$761$	5.89468e47			1.68894			0.844468	−	0.535606i	$-0.179917\pi$
$761$	5.89468e47			1.68894			0.844468	+	0.535606i	$0.179917\pi$
$762$			6.60326e46i			0.185140i
$763$		−	9.85611e45i		−	0.0270427i
$764$	3.07479e47			0.825609
$765$	−3.12693e46	+	1.34218e46i	−0.0821684	+	0.0352694i
$766$	−3.07895e46			−0.0791822
$767$		−	2.11959e46i		−	0.0533493i
$768$			1.87670e47i			0.462311i
$769$	−2.00353e47			−0.483071			−0.241536	−	0.970392i	$-0.577651\pi$
$769$	−2.00353e47			−0.483071			−0.241536	+	0.970392i	$0.577651\pi$
$770$	1.85390e46	+	4.31910e46i	0.0437512	+	0.101929i
$771$	2.39262e47			0.552682
$772$			2.48034e47i			0.560822i
$773$		−	7.65303e45i		−	0.0169384i	−0.999964	−	0.00846919i	$-0.997304\pi$
$773$		−	7.65303e45i		−	0.0169384i	0.999964	−	0.00846919i	$-0.00269586\pi$
$774$	−2.84417e47			−0.616212
$775$	7.54932e46	−	7.94455e46i	0.160114	−	0.168497i
$776$	−1.53136e47			−0.317950
$777$			7.84714e46i			0.159501i
$778$		−	3.41339e46i		−	0.0679239i
$779$	−1.05942e48			−2.06396
$780$	−4.73170e45	−	1.10236e46i	−0.00902518	−	0.0210263i
$781$	3.73281e47			0.697097
$782$		−	9.85228e45i		−	0.0180146i
$783$			3.85841e47i			0.690780i
$784$	−8.82731e46			−0.154744
$785$	3.49417e45	−	1.49981e45i	0.00599784	−	0.00257447i
$786$	1.56291e47			0.262701
$787$			3.82823e47i			0.630108i	0.949074	+	0.315054i	$0.102023\pi$
$787$			3.82823e47i			0.630108i	−0.949074	+	0.315054i	$0.897977\pi$
$788$			2.88824e46i			0.0465534i
$789$	9.14732e46			0.144385
$790$	−3.05687e47	+	1.31211e47i	−0.472531	+	0.202826i
$791$	2.42249e47			0.366733
$792$		−	4.04961e47i		−	0.600410i
$793$		−	5.29239e46i		−	0.0768501i
$794$	7.28214e47			1.03567
$795$	−1.27798e47	−	2.97736e47i	−0.178019	−	0.414738i
$796$	−9.93277e46			−0.135520
$797$		−	5.46986e47i		−	0.730994i	−0.930812	−	0.365497i	$-0.880899\pi$
$797$		−	5.46986e47i		−	0.730994i	0.930812	−	0.365497i	$-0.119101\pi$
$798$			8.31308e46i			0.108821i
$799$	−6.77643e46			−0.0868918
$800$	−5.38345e47	−	5.11563e47i	−0.676201	−	0.642560i
$801$	5.72426e47			0.704341
$802$		−	6.40344e47i		−	0.771856i
$803$			3.42701e46i			0.0404677i
$804$	3.53313e47			0.408729
$805$	−1.93992e46	−	4.51950e46i	−0.0219863	−	0.0512222i
$806$	−1.37228e46			−0.0152375
$807$		−	5.16050e47i		−	0.561408i
$808$		−	8.80119e47i		−	0.938110i
$809$	−6.85674e47			−0.716089			−0.358045	−	0.933704i	$-0.616556\pi$
$809$	−6.85674e47			−0.716089			−0.358045	+	0.933704i	$0.616556\pi$
$810$	−2.83904e47	+	1.21861e47i	−0.290515	+	0.124699i
$811$	1.01450e48			1.01720			0.508602	−	0.861002i	$-0.330162\pi$
$811$	1.01450e48			1.01720			0.508602	+	0.861002i	$0.330162\pi$
$812$		−	1.11732e47i		−	0.109775i
$813$			6.34237e47i			0.610601i
$814$	8.07711e47			0.761997
$815$	9.16199e47	−	3.93263e47i	0.847012	−	0.363566i
$816$	−8.66614e45			−0.00785124
$817$			2.02547e48i			1.79830i
$818$			5.49037e47i			0.477718i
$819$	2.12701e46			0.0181378
$820$	−3.30197e47	−	7.69272e47i	−0.275959	−	0.642912i
$821$	−1.33191e48			−1.09097			−0.545486	−	0.838120i	$-0.683655\pi$
$821$	−1.33191e48			−1.09097			−0.545486	+	0.838120i	$0.683655\pi$
$822$		−	6.61695e47i		−	0.531218i
$823$		−	4.48712e47i		−	0.353078i	−0.984294	−	0.176539i	$-0.943510\pi$
$823$		−	4.48712e47i		−	0.353078i	0.984294	−	0.176539i	$-0.0564901\pi$
$824$	2.14953e48			1.65785
$825$	−2.96396e47	−	2.81651e47i	−0.224070	−	0.212922i
$826$	−1.16065e47			−0.0860064
$827$			7.36744e47i			0.535150i	0.963537	+	0.267575i	$0.0862223\pi$
$827$			7.36744e47i			0.535150i	−0.963537	+	0.267575i	$0.913778\pi$
$828$			1.49011e47i			0.106101i
$829$	−2.69972e48			−1.88438			−0.942191	−	0.335077i	$-0.891238\pi$
$829$	−2.69972e48			−1.88438			−0.942191	+	0.335077i	$0.891238\pi$
$830$	5.00401e47	+	1.16580e48i	0.342397	+	0.797694i
$831$	−1.09016e48			−0.731264
$832$			1.17078e47i			0.0769908i
$833$			1.62004e47i			0.104444i
$834$	2.16632e47			0.136925
$835$	1.12664e48	−	4.83591e47i	0.698166	−	0.299676i
$836$	−1.01412e48			−0.616151
$837$			3.07543e47i			0.183204i
$838$			5.56614e47i			0.325108i
$839$	−1.22574e48			−0.701980			−0.350990	−	0.936379i	$-0.614155\pi$
$839$	−1.22574e48			−0.701980			−0.350990	+	0.936379i	$0.614155\pi$
$840$	−1.71658e47	+	7.36815e46i	−0.0963956	+	0.0413762i
$841$	−4.21129e47			−0.231890
$842$		−	6.12524e47i		−	0.330730i
$843$			1.14836e48i			0.608026i
$844$	1.60986e48			0.835866
$845$	7.67382e47	+	1.78780e48i	0.390729	+	0.910295i
$846$	−8.64766e47			−0.431805
$847$		−	2.33859e47i		−	0.114519i
$848$			3.52863e47i			0.169463i
$849$	−1.12911e48			−0.531811
$850$	1.11295e47	−	1.17122e47i	0.0514120	−	0.0541036i
$851$	−8.45188e47			−0.382927
$852$			5.21693e47i			0.231826i
$853$		−	2.46709e48i		−	1.07529i	−0.843171	−	0.537645i	$-0.819314\pi$
$853$		−	2.46709e48i		−	1.07529i	0.843171	−	0.537645i	$-0.180686\pi$
$854$	−2.89802e47			−0.123893
$855$	1.21977e48	+	2.84175e48i	0.511491	+	1.19164i
$856$	−1.04100e48			−0.428188
$857$			1.57881e48i			0.637008i	0.947921	+	0.318504i	$0.103181\pi$
$857$			1.57881e48i			0.637008i	−0.947921	+	0.318504i	$0.896819\pi$
$858$			5.11972e46i			0.0202631i
$859$	4.06189e48			1.57703			0.788517	−	0.615013i	$-0.210849\pi$
$859$	4.06189e48			1.57703			0.788517	+	0.615013i	$0.210849\pi$
$860$	−1.47074e48	+	6.31291e47i	−0.560160	+	0.240439i
$861$	−3.47103e47			−0.129690
$862$		−	3.57576e48i		−	1.31069i
$863$		−	2.97250e48i		−	1.06891i	−0.845195	−	0.534457i	$-0.820516\pi$
$863$		−	2.97250e48i		−	1.06891i	0.845195	−	0.534457i	$-0.179484\pi$
$864$	2.08400e48			0.735225
$865$	5.23592e48	−	2.24743e48i	1.81229	−	0.777894i
$866$	−1.70028e48			−0.577396
$867$		−	1.29072e48i		−	0.430048i
$868$		−	8.90586e46i		−	0.0291139i
$869$	−1.68261e48			−0.539707
$870$	−3.23478e47	−	7.53619e47i	−0.101807	−	0.237183i
$871$	5.43191e47			0.167746
$872$		−	4.03202e47i		−	0.122180i
$873$			8.30591e47i			0.246975i
$874$	−8.95373e47			−0.261256
$875$	2.79927e47	−	7.56410e47i	0.0801515	−	0.216583i
$876$	−4.78955e46			−0.0134579
$877$			2.87186e48i			0.791900i	0.918272	+	0.395950i	$0.129585\pi$
$877$			2.87186e48i			0.791900i	−0.918272	+	0.395950i	$0.870415\pi$
$878$		−	1.99103e48i		−	0.538789i
$879$	6.39273e47			0.169774
$880$	1.75638e47	+	4.09189e47i	0.0457776	+	0.106650i
$881$	−4.74319e47			−0.121330			−0.0606650	−	0.998158i	$-0.519322\pi$
$881$	−4.74319e47			−0.121330			−0.0606650	+	0.998158i	$0.519322\pi$
$882$			2.06740e48i			0.519030i
$883$		−	6.06557e48i		−	1.49458i	−0.664496	−	0.747292i	$-0.731354\pi$
$883$		−	6.06557e48i		−	1.49458i	0.664496	−	0.747292i	$-0.268646\pi$
$884$	2.39770e46			0.00579873
$885$	9.27808e47	−	3.98246e47i	0.220239	−	0.0945338i
$886$	−2.54013e48			−0.591833
$887$		−	4.64999e48i		−	1.06344i	−0.846921	−	0.531719i	$-0.821546\pi$
$887$		−	4.64999e48i		−	1.06344i	0.846921	−	0.531719i	$-0.178454\pi$
$888$			3.21017e48i			0.720633i
$889$	−6.58846e47			−0.145179
$890$	−2.49756e48	+	1.07204e48i	−0.540233	+	0.231886i
$891$	−1.56271e48			−0.331815
$892$			3.50705e48i			0.731007i
$893$			6.15840e48i			1.26014i
$894$	7.45849e45			0.00149824
$895$	−3.10344e48	−	7.23019e48i	−0.612016	−	1.42584i
$896$	−4.71584e47			−0.0913013
$897$		−	5.35727e46i		−	0.0101828i
$898$			6.51054e47i			0.121495i
$899$	1.11187e48			0.203713
$900$	−1.68329e48	+	1.77141e48i	−0.302801	+	0.318653i
$901$	6.47595e47			0.114378
$902$			3.57275e48i			0.619577i
$903$			6.63613e47i			0.112997i
$904$	9.91012e48			1.65691
$905$	3.35790e48	+	7.82301e48i	0.551272	+	1.28432i
$906$	1.14958e48			0.185320
$907$		−	1.71333e48i		−	0.271219i	−0.990762	−	0.135610i	$-0.956701\pi$
$907$		−	1.71333e48i		−	0.271219i	0.990762	−	0.135610i	$-0.0432993\pi$
$908$			4.08769e48i			0.635421i
$909$	−4.77365e48			−0.728697
$910$	−9.28037e46	+	3.98344e46i	−0.0139118	+	0.00597139i
$911$	6.80039e48			1.00111			0.500553	−	0.865706i	$-0.333130\pi$
$911$	6.80039e48			1.00111			0.500553	+	0.865706i	$0.333130\pi$
$912$			7.87577e47i			0.113862i
$913$			6.41699e48i			0.911095i
$914$	−1.59685e48			−0.222665
$915$	2.31664e48	−	9.94377e47i	0.317256	−	0.136177i
$916$	−4.88645e48			−0.657232
$917$			1.55941e48i			0.205999i
$918$			4.53393e47i			0.0588262i
$919$	−1.53654e49			−1.95811			−0.979056	−	0.203593i	$-0.934738\pi$
$919$	−1.53654e49			−1.95811			−0.979056	+	0.203593i	$0.934738\pi$
$920$	−7.93598e47	−	1.84887e48i	−0.0993348	−	0.231424i
$921$	3.32099e47			0.0408304
$922$			3.89946e48i			0.470917i
$923$			8.02062e47i			0.0951436i
$924$	−3.32261e47			−0.0387162
$925$	−1.00474e49	−	9.54758e48i	−1.15005	−	1.09283i
$926$	5.20736e48			0.585513
$927$		−	1.16588e49i		−	1.28777i
$928$		−	7.53435e48i		−	0.817531i
$929$	3.67102e47			0.0391316			0.0195658	−	0.999809i	$-0.493772\pi$
$929$	3.67102e47			0.0391316			0.0195658	+	0.999809i	$0.493772\pi$
$930$	−2.57835e47	−	6.00688e47i	−0.0270006	−	0.0629043i
$931$	1.47229e49			1.51469
$932$		−	4.54258e48i		−	0.459135i
$933$			5.31767e47i			0.0528049i
$934$	2.63842e48			0.257407
$935$	7.50968e47	−	3.22341e47i	0.0719830	−	0.0308975i
$936$	8.70133e47			0.0819472
$937$			6.55944e48i			0.606964i	0.952837	+	0.303482i	$0.0981493\pi$
$937$			6.55944e48i			0.606964i	−0.952837	+	0.303482i	$0.901851\pi$
$938$		−	2.97442e48i		−	0.270430i
$939$	−7.96507e48			−0.711553
$940$	−4.47177e48	+	1.91943e48i	−0.392527	+	0.168486i
$941$	1.21575e49			1.04861			0.524306	−	0.851530i	$-0.324325\pi$
$941$	1.21575e49			1.04861			0.524306	+	0.851530i	$0.324325\pi$
$942$		−	2.26802e46i		−	0.00192224i
$943$		−	3.73852e48i		−	0.311356i
$944$	−1.09959e48			−0.0899900
$945$	8.92733e47	+	2.07983e48i	0.0717954	+	0.167264i
$946$	6.83061e48			0.539828
$947$		−	1.65747e49i		−	1.28728i	−0.765329	−	0.643639i	$-0.777424\pi$
$947$		−	1.65747e49i		−	1.28728i	0.765329	−	0.643639i	$-0.222576\pi$
$948$		−	2.35160e48i		−	0.179484i
$949$	−7.36355e46			−0.00552325
$950$	−1.06440e49	−	1.01145e49i	−0.784632	−	0.745598i
$951$	3.09548e48			0.224259
$952$		−	3.73368e47i		−	0.0265844i
$953$			6.56420e48i			0.459356i	0.973267	+	0.229678i	$0.0737673\pi$
$953$			6.56420e48i			0.459356i	−0.973267	+	0.229678i	$0.926233\pi$
$954$	8.26421e48			0.568399
$955$	8.88191e48	+	2.06925e49i	0.600414	+	1.39881i
$956$	1.04173e49			0.692149
$957$		−	4.14819e48i		−	0.270901i
$958$		−	4.54428e48i		−	0.291698i
$959$	6.60212e48			0.416559
$960$	−5.12483e48	+	2.19975e48i	−0.317837	+	0.136426i
$961$	−1.55172e49			−0.945972
$962$			1.73551e48i			0.104001i
$963$			5.64626e48i			0.332604i
$964$	3.78130e48			0.218963
$965$	−1.66920e49	+	7.16477e48i	−0.950186	+	0.407851i
$966$	−2.93355e47			−0.0164161
$967$			2.72573e49i			1.49950i	0.661721	+	0.749751i	$0.269827\pi$
$967$			2.72573e49i			1.49950i	−0.661721	+	0.749751i	$0.730173\pi$
$968$		−	9.56691e48i		−	0.517402i
$969$	1.44541e48			0.0768508
$970$	−1.55553e48	−	3.62396e48i	−0.0813099	−	0.189431i
$971$	−2.17486e47			−0.0111767			−0.00558835	−	0.999984i	$-0.501779\pi$
$971$	−2.17486e47			−0.0111767			−0.00558835	+	0.999984i	$0.501779\pi$
$972$		−	1.06450e49i		−	0.537837i
$973$			2.16146e48i			0.107371i
$974$	−1.18429e49			−0.578408
$975$	6.05179e47	−	6.36862e47i	0.0290608	−	0.0305822i
$976$	−2.74557e48			−0.129631
$977$			1.03056e49i			0.478426i	0.970967	+	0.239213i	$0.0768894\pi$
$977$			1.03056e49i			0.478426i	−0.970967	+	0.239213i	$0.923111\pi$
$978$		−	5.94693e48i		−	0.271457i
$979$	−1.37475e49			−0.617033
$980$	4.58879e48	+	1.06907e49i	0.202520	+	0.471818i
$981$	−2.18691e48			−0.0949059
$982$			2.61623e49i			1.11644i
$983$			6.87428e47i			0.0288466i	0.999896	+	0.0144233i	$0.00459123\pi$
$983$			6.87428e47i			0.0288466i	−0.999896	+	0.0144233i	$0.995409\pi$
$984$	−1.41996e49			−0.585944
$985$	−1.94371e48	+	8.34306e47i	−0.0788741	+	0.0338554i
$986$	1.63917e48			0.0654116
$987$			2.01770e48i			0.0791816i
$988$		−	2.17903e48i		−	0.0840956i
$989$	−7.14754e48			−0.271280
$990$	9.58340e48	−	4.11351e48i	0.357716	−	0.153544i
$991$	3.45059e48			0.126671			0.0633356	−	0.997992i	$-0.479826\pi$
$991$	3.45059e48			0.126671			0.0633356	+	0.997992i	$0.479826\pi$
$992$		−	6.00541e48i		−	0.216820i
$993$		−	1.04020e49i		−	0.369365i
$994$	4.39195e48			0.153385
$995$	−2.86921e48	−	6.68450e48i	−0.0985556	−	0.229608i
$996$	−8.96833e48			−0.302993
$997$			3.48409e49i			1.15776i	0.815412	+	0.578881i	$0.196510\pi$
$997$			3.48409e49i			1.15776i	−0.815412	+	0.578881i	$0.803490\pi$
$998$		−	1.76306e48i		−	0.0576253i
$999$	3.88948e49			1.25043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.11	yes	16
5.2	odd	4		25.34.a.f.1.6		16
5.3	odd	4		25.34.a.f.1.11		16
5.4	even	2	inner	5.34.b.a.4.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.6	✓	16	5.4	even	2	inner
5.34.b.a.4.11	yes	16	1.1	even	1	trivial
25.34.a.f.1.6		16	5.2	odd	4
25.34.a.f.1.11		16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+62697.7i q^{2} -3.24591e7i q^{3} +4.65894e9 q^{4} +(1.34579e11 + 3.13534e11i) q^{5} +2.03511e12 q^{6} +2.03055e13i q^{7} +8.30673e14i q^{8} +4.50547e15 q^{9} +O(q^{10})\)	\(q+62697.7i q^{2} -3.24591e7i q^{3} +4.65894e9 q^{4} +(1.34579e11 + 3.13534e11i) q^{5} +2.03511e12 q^{6} +2.03055e13i q^{7} +8.30673e14i q^{8} +4.50547e15 q^{9} +(-1.96579e16 + 8.43781e15i) q^{10} -1.08204e17 q^{11} -1.51225e17i q^{12} -2.32496e17i q^{13} -1.27311e18 q^{14} +(1.01770e19 - 4.36832e18i) q^{15} -1.20613e19 q^{16} +2.21357e19i q^{17} +2.82482e20i q^{18} +2.01169e21 q^{19} +(6.26996e20 + 1.46074e21i) q^{20} +6.59098e20 q^{21} -6.78414e21i q^{22} +7.09891e21i q^{23} +2.69629e22 q^{24} +(-8.01921e22 + 8.43905e22i) q^{25} +1.45770e22 q^{26} -3.26686e23i q^{27} +9.46020e22i q^{28} -1.18108e24 q^{29} +(2.73884e23 + 6.38077e23i) q^{30} -9.41403e23 q^{31} +6.37921e24i q^{32} +3.51220e24i q^{33} -1.38786e24 q^{34} +(-6.36647e24 + 2.73270e24i) q^{35} +2.09907e25 q^{36} +1.19059e26i q^{37} +1.26128e26i q^{38} -7.54661e24 q^{39} +(-2.60445e26 + 1.11791e26i) q^{40} -5.26633e26 q^{41} +4.13239e25i q^{42} +1.00685e27i q^{43} -5.04115e26 q^{44} +(6.06343e26 + 1.41262e27i) q^{45} -4.45085e26 q^{46} +3.06131e27i q^{47} +3.91500e26i q^{48} +7.31868e27 q^{49} +(-5.29109e27 - 5.02786e27i) q^{50} +7.18505e26 q^{51} -1.08318e27i q^{52} -2.92557e28i q^{53} +2.04824e28 q^{54} +(-1.45620e28 - 3.39257e28i) q^{55} -1.68672e28 q^{56} -6.52976e28i q^{57} -7.40509e28i q^{58} +9.11668e28 q^{59} +(4.74142e28 - 2.03517e28i) q^{60} +2.27634e29 q^{61} -5.90238e28i q^{62} +9.14857e28i q^{63} -5.03568e29 q^{64} +(7.28955e28 - 3.12892e28i) q^{65} -2.20207e29 q^{66} +2.33634e30i q^{67} +1.03129e29i q^{68} +2.30424e29 q^{69} +(-1.71334e29 - 3.99163e29i) q^{70} -3.44979e30 q^{71} +3.74257e30i q^{72} -3.16717e29i q^{73} -7.46471e30 q^{74} +(2.73924e30 + 2.60296e30i) q^{75} +9.37233e30 q^{76} -2.19713e30i q^{77} -4.73155e29i q^{78} +1.55504e31 q^{79} +(-1.62321e30 - 3.78165e30i) q^{80} +1.44422e31 q^{81} -3.30187e31i q^{82} -5.93046e31i q^{83} +3.07069e30 q^{84} +(-6.94030e30 + 2.97901e30i) q^{85} -6.31272e31 q^{86} +3.83367e31i q^{87} -8.98822e31i q^{88} +1.27051e32 q^{89} +(-8.85679e31 + 3.80163e31i) q^{90} +4.72095e30 q^{91} +3.30734e31i q^{92} +3.05571e31i q^{93} -1.91937e32 q^{94} +(2.70732e32 + 6.30733e32i) q^{95} +2.07063e32 q^{96} +1.84352e32i q^{97} +4.58864e32i q^{98} -4.87509e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

Introduction

L-functions

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